Heidelberg TDA Seminar (Summer 2023)

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In recent years there has been a somewhat surprising flow of ideas from the mathematical branch of topology towards applications in the natural sciences. The tale of Topological Data Analysis (TDA) has it, that these methods provide a highly flexible, nonparametric approach to data analysis. Indeed, there are by now several well-known mathematical results that make statements of this kind rigorous. However, successful applications of TDA often build on a deep intuition about the system in question and many theoretical aspects of TDA remain active fields of research.

The goal of this seminar is to bring together people from various backgrounds who are interested in TDA. We will have talks on topics ranging from applications of TDA on real world problems to the abstract mathematical foundations of the subject. An emphasis is put on synergies with Machine Learning. In addition, we aim to discuss works, which are inspired by TDA but not employing it directly. Contributions by participants are very welcome!

Coordinates and Organization

Time: Thursdays 11h15 - 12h45
Location: Mathematikon (INF205), 00.200 (ground floor)

Organizers: Freya Bretz, Lukas Hahn, Daniel Spitz.
Feel free to get in touch with us in the case of questions: structures-hiwi@mathi.uni-heidelberg.de

Schedule

The following schedule is preliminary; in particular topics can be still subject to slight changes.

Date Topic Info Speaker Slides
27.04. Preliminary meeting (exceptionally in SR Statistik, 02.104!)
04.05. No TDA Seminar session
11.05. Persistent homology of quantum entanglement (based on arxiv:2110.10214) Daniel Spitz
18.05. No TDA Seminar session (Himmelfahrt)
25.05. Metrizing multiparameter modules Lukas Waas
01.06. TBA
08.06. No TDA Seminar session (Fronleichnam)
15.06. TBA Sebastian Damrich
22.06. TBA Tobias Buck
29.06. Literature approaches: TDA in conjunction with Machine Learning Lukas Hahn
06.07. On-the-hands coding with TDA and Machine Learning Lukas Hahn
13.07. SPD matrices and Machine Learning Michael Bleher
20.07. Mayer-Vietoris for persistent homology Freya Bretz